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"With satisfaction with democracy at an all-time low in this country, I really do hope that 2017 heralds a new way of doing things for the Turnbull government and for politics in general," he wrote on Facebook.

"What the Turnbull government needs to do is start being more loyal to the voters and the party members who sent us here or there will come a time when remaining inside the tent is no longer tenable to my conscience or my voters."

Senator Bernardi and Gina Rinehart met key members of incoming US president Donald Trump's team, sparking fears of a split bankrolled by the mining magnate, The Australian reported on Thursday.

But the South Australian senator dismissed renewed suggestions he was poised to leave the Liberals as gossip and speculation.

Government backbencher Luke Howarth said his message was for Senator Bernardi to stick with the Liberals.

"My advice to him would be: stay in the Liberal Party, keep advocating for the issues that you think are important to Australians and remain in the tent," he told Sky News.

"We need you in the Liberal Party ... we're a diverse party and I think that's healthy."

Senator Bernardi set up the Australian Conservatives movement after the July federal election to rival the left-wing protest and campaigning group GetUp.

A Christmas message on the conservative group's website says more than 60,000 Australians have signed up to its mailing list despite it operating with "modest staff numbers and a bare bones website".

"This is all set to change in 2017," it says, promising a state-of-the-art website and "a number of important campaigns".

Former prime minister Tony Abbott said Senator Bernardi was right to say it was best for the Australian people to have a "strong, cohesive and sound Liberal Party".

"To be strong & united, the Liberal Party cannot take the base for granted & must convincingly argue for its values & principles," he wrote on Twitter.